Do Closed Timelike Curves Exist?

[twoface42]

im doing my project for school on this a need help.

 

[JesseM]

For reference, twoface42 and I already had some discussion of this by PM, so people can see if they have anything they want to add or if I made any mistakes in my comments:

There's no evidence they exist in reality, although as you say there are metrics in general relativity in which they occur (the Godel metric requires the entire universe to be rotating which doesn't seem to match observations, but the 'traversable wormhole' metric could also include CTCs, see http://www.newscientist.com/article/mg12617144.500-wormholes-time-travel-and-quantum-gravity.html for more info); but some approaches to quantum gravity suggest that a future theory of quantum gravity (which would replace general relativity, a non-quantum theory of gravity) would rule them out. For a little more on this see http://en.wikipedia.org/wiki/Chronology_protection_conjecture and http://members.fortunecity.com/sparck/TimeTravelPossible.htm and http://groups.google.com/group/alt.sci.time-travel/msg/fc5fefa6578822ee

and on a question about the Kerr metric:

The Kerr metric represents an idealized rotating black hole, with nothing else in the universe. There is a region that can contain closed timelike curves here, but it's inside the event horizon near the "ring singularity" at the center (inside what is called the 'Cauchy horizon' or 'inner horizon' of the black hole, distinct from the 'outer horizon' which marks the point where light can't escape), cut off from the outside universe (although it's speculated that GR might allow this region to be connected to the inside of a 'white hole' that expels matter out into a different universe, or a different region of spacetime). There are questions about whether this metric is stable against perturbations, so it may be that the gravity from even a small infalling object would disrupt the ring singularity and the Cauchy horizon and cause them to collapse to a point singularity like the one at the center of a nonrotating black hole. http://www.valdostamuseum.org/hamsmith/BlackHole.html has a section called "Is such a journey physically reasonable?" where they write:

As Wald says, "... we would, in general, expect a complicated dynamical evolution which only settles down to a stationary geometry at late times ... Thus, we are not in a position to follow the dynamical evolution of the gravitational collapse of a body which forms a Kerr Black Hole and thereby determine the detailed SpaceTime geometry inside the Black Hole. ...", so we really don't know the answer.

Wald is pessimistic, saying: "... there is good reason to believe that in a physically realistic case ... the Cauchy Horizon r = r- ... will become a true, physical singularity ...".

Wald's pessimism is supported by Hod and Piran in gr-qc/9803004, who "... study the inner-structure of a charged black-hole which is formed from the gravitational collapse of a self-gravitating charged scalar-field ...". According to http://www.aip.org/enews/physnews/1998/split/pnu386-1.htm , Hod and Piran "... have now supported previous indications showing that these Cauchy horizons are unstable; small disturbances in the black hole instantly transform them into singularity regions. In fact, their calculations suggest that generic black holes contain two singularities that are connected to each other so that all infalling matter reaches one or the other. ..."

However, I do not agree that the results of such calculations, which due to computational difficulty deal with very simplified structures, are applicable in all physically reasonable cases. Therefore, I am optimistic that such a journey might be physically reasonable.

Another issue is that with a Kerr black hole, an infalling observer would theoretically be able to see the entire infinite future history of the universe in a finite time, which means an infinite amount of radiation must be hitting certain inner regions of the black hole, which again raises questions about whether they could possibly be stable or realistic. This page from the Usenet Physics FAQ says:

Will you see the universe end?

If an external observer sees me slow down asymptotically as I fall, it might seem reasonable that I'd see the universe speed up asymptotically-- that I'd see the universe end in a spectacular flash as I went through the horizon. This isn't the case, though. What an external observer sees depends on what light does after I emit it. What I see, however, depends on what light does before it gets to me. And there's no way that light from future events far away can get to me. Faraway events in the arbitrarily distant future never end up on my "past light-cone," the surface made of light rays that get to me at a given time.

That, at least, is the story for an uncharged, nonrotating black hole. For charged or rotating holes, the story is different. Such holes can contain, in the idealized solutions, "timelike wormholes" which serve as gateways to otherwise disconnected regions-- effectively, different universes. Instead of hitting the singularity, I can go through the wormhole. But at the entrance to the wormhole, which acts as a kind of inner event horizon, an infinite speed-up effect actually does occur. If I fall into the wormhole I see the entire history of the universe outside play itself out to the end. Even worse, as the picture speeds up the light gets blueshifted and more energetic, so that as I pass into the wormhole an "infinite blueshift" happens which fries me with hard radiation. There is apparently good reason to believe that the infinite blueshift would imperil the wormhole itself, replacing it with a singularity no less pernicious than the one I've managed to miss. In any case it would render wormhole travel an undertaking of questionable practicality.

And in response to a question about whether any CTCs in a rotating black hole would be sealed off from the outside universe:

We couldn't escape back out from the outer event horizon which we entered from, but there is an idea called "geodesic completeness" which postulates that spacetime can only "end" at a singularity, it turns out that if you apply this principle to the metric of an idealized eternal black hole (rotating or nonrotating), you're forced to conclude that the region inside the event horizon is shared in common with the region inside a different black-hole-like object. In the case of a rotating black hole this would mean you could fall through the outer horizon (which is impossible to escape back out from the normal way), fall through the inner horizon, but then inside the inner horizon the gravity from the ring singularity actually seems repulsive (apparently this is part of the reason why it's difficult to see how such a ring singularity could ever form in the real universe, see the last section of this page), so you could escape back out from the inner horizon and you'd theoretically end up inside the outer horizon of a "white hole", a hypothetical object that would be the reverse of a black hole, spitting matter out and with it being impossible to enter the white hole's event horizon from the outside. In the simple Kerr metric this white hole would actually lead to another universe altogether, although apparently it's not hard to come up with a modified metric where the white hole would just be in a different region of our universe (though there is no evidence for astrophysical white holes anywhere in the real world).

In the case of an idealized nonrotating black hole, a "Schwarzschild black hole" which should really be called a "grey hole" since it can spit matter out as well as pull it in, any observer falling into the event horizon will find themselves in the inner black hole region (separate from the inner region of spacetime where matter is being spit out), and inside they can meet infalling objects from a different black hole in another universe (although again, the metric can be modified so it's a different black hole in our universe), though they will still all be crushed at the singularity so unlike with Kerr black holes this doesn't offer the possibility of escape. The Schwarzschild black hole is an idealization though, it has existed for an infinite time in the past and will continue to exist for an infinite time in the future, whereas real astrophysical black holes would all have formed at some definite time and so they wouldn't need to be connected to another universe this way.

A useful way of picturing this stuff is a Penrose diagram--see http://en.wikipedia.org/wiki/Image:PENROSE2.PNG for one that shows both a nonrotating "grey" hole in the Schwarzschild metric, and a rotating black hole in the Kerr metric. And I also found this page which has a good discussion of the Kerr metric, and includes a similar Penrose diagram.

By the way, looking into this a bit more, I think I was wrong that closed timelike curves are possible anywhere inside the inner horizon. Instead, I think a traveler must actually cross through the center of the ring singularity (like jumping through a hoop) to enter a region of "negative space" where they become possible, and I don't know if it's possible to escape back out the way you came in this region, or even to escape into another universe. http://casa.colorado.edu/~ajsh/astr2030_05/summaries.html says:

Rotating black holes
*The Kerr-Newman (KN) geometry describes the geometry of empty space around a spinning, possibly charged, black hole.
*Real black holes probably spin.
*Centrifugal force causes the KN geometry to be gravitationally repulsive in its core.
*The phenomenology of the KN geometry is quite similar to that of the RN geometry: the gravitational repulsion causes the KN geometry to have both inner and outer horizons, and black hole-wormhole-white hole connections to new universes.
*The KN geometry is, again, inconsistent, because the black hole cannot be empty in its core if the core is repulsive.
*The singularity of the KN geometry forms a ring, kept open by the centrifugal force.
*The outer horizon and inner horizon are confocal ellipsoids, with the ring singularity at the focus.
*The other side of the disk bounded by the ring singularity is a new region, the "antiverse", at negative radius. In the antiverse, the black hole appears to have negative mass.
*In the antiverse, circles around the axis near the disk are timelike. These circles form "closed timelike loops" (CTLs), where time keeps repeating itself.

And this page and this section of a wikipedia article say the same thing, that you can only get to the CTC region by going through the ring singularity.

And one other thing I wasn't sure about:

But after looking at some of the other articles I sent you, I'm not sure if the idea of the singularity being "unstable" is that outside matter falling in would disrupt it, or if it has more to do with the idea that gravity is repulsive inside the inner horizon, which might mean the ring singularity wouldn't form in the first place. If you want to know more about this stuff I recommend starting a thread in the main forums, like I said I'm not an expert.

 

[George Jones]

im doing my project for school on this a need help.

At what level are you in school?

Adding a little to what JesseM wrote, here

https://www.physicsforums.com/showthread.php?p=1068268#post1068268

are some general thoughts on time travel, including a little on

Will Quantum Gravity Prevent Closed Timelike Curves?

It seems that we won't know the role of quantum gravity until we have a workable quantum theory of gravity.

Here

https://www.physicsforums.com/showthread.php?p=1166705#post1166705

is a mathematical demonstration of closed timelike curves in the spacetime of a rotating black hole. There does exists a closed timelike curve through any event inside the inner horizon, but I am not sure if all of these curves pass through the ring. Israel and Poisson (and others) have done work on what happens inside rotating black holes that might be relevant.

Here

https://www.physicsforums.com/showthread.php?p=1254758#post1254758

is a proof that any compact (in the mathematical sense) spacetime contains closed timelike curves.

 

[MeJennifer]

There are questions about whether this metric is stable against perturbations, so it may be that the gravity from even a small infalling object would disrupt the ring singularity and the Cauchy horizon and cause them to collapse to a point singularity like the one at the center of a nonrotating black hole.

A chicken and egg argument. A Kerr metric is a vacuum solution so there is nothing available to perturb. If you assume a spacetime with such additional mass-energies then you obviously cannot use the Kerr metric. And weak field approximations are obviously useless in those models since the curvature is too strong for that.

Another issue is that with a Kerr black hole, an infalling observer would theoretically be able to see the entire infinite future history of the universe in a finite time, which means an infinite amount of radiation must be hitting certain inner regions of the black hole, which again raises questions about whether they could possibly be stable or realistic.

Same chicken and egg argument as above, if the spacetime contains radiation the Kerr solution is obviously the wrong solution.

 

[JesseM]

A chicken and egg argument. A Kerr metric is a vacuum solution so there is nothing available to perturb. If you assume a spacetime with such additional mass-energies then you obviously cannot use the Kerr metric. And weak field approximations are obviously useless in those models since the curvature is too strong for that.

A perturbation of the Kerr metric would obviously result in a somewhat different metric, but that's what perturbation means, you're making a slight change and seeing the result. I imagine this is different from the weak-field approximation, since as you say spacetime is highly curved in the neighborhood of a rotating black hole. Physicists do talk about perturbations of the Kerr metric...for example, this book says:

Exactly as for Schwarzschild black holes, one can generate all non-trivial features of a perturbing field from the solution $$\psi$$ to (4.8.1) [Wald (1973)]. Moreover, Chrzanowski (1975) has shown how the perturbed metric is obtained from $$\Psi_0$$ and $$\Psi_4$$ (see Appendix G.6 for more details). This completes the perturbation picture for Kerr black holes. The method of separation of variables has been used to analyze the stability of the Kerr metric and to study the scattering of electromagnetic, gravitational and neutrino fields by Kerr black holes.

Likewise, have a look at the first page of http://www.jstor.org/pss/79484, which considers "linear perturbations of black hole models by a variety of fields" and uses this to "discuss the internal stability of the Kerr and Reissner-Nordström black hole solutions", saying "These models have highly peculiar, if not disturbing, features in their interiors. The question we would like to be able to answer is whether these features actually manifest themselves in nature or are purely a product of the exact symmetry of the model".

Other papers discussing the stability of Kerr black holes against perturbations:

http://www.jstor.org/pss/78810

http://adsabs.harvard.edu/full/1973ApJ...185..649P

http://arxiv.org/abs/gr-qc/9803004

http://arxiv.org/abs/gr-qc/9902008

 

[JesseM]

Here

https://www.physicsforums.com/showthread.php?p=1166705#post1166705

is a mathematical demonstration of closed timelike curves in the spacetime of a rotating black hole. There does exists a closed timelike curve through any event inside the inner horizon, but I not sure if all of these curves pass through the ring. Israel and Poisson (and others) have done work on what happens inside rotating black holes that might be relevant.

When looking for information on Kerr black holes and CTCs, I came across this paper which suggests that the apparent CTCs are just an artifact of a bad choice of coordinates, and with a different choice they disappear (and so are not really physical):

http://arxiv.org/abs/gr-qc/0207014

If you feel like giving it a once-over, I'd be interested to know if you think the argument can be dismissed out of hand, or if there could possibly be something to it.

 

[twoface42]

JesseM so the paper you sent me kind of confussed me,does it say ctc's are real or not?

 

[JesseM]

JesseM so the paper you sent me kind of confussed me,does it say ctc's are real or not?

The paper I just posted above claims to show that they don't actually happen inside the inner event horizon of the Kerr metric for a rotating black hole. But papers on arxiv.org are not peer-reviewed, and this claim contradicts a lot of previous studies of the Kerr metric, so I'd be cautious about accepting it.

 

[twoface42]

you said the paper condradicts other's,like what?, you also said the claims show that they don't actually happen inside the inner event horizon of the Kerr metric for a rotating black hole,do they appear in some other region of a black hole or not at all?

 

[JesseM]

you said the paper condradicts other's,like what?

All the previous papers and books which try to prove the Kerr metric does contain CTCs...George Jones linked to this post which is based on a textbook, for example. You can find a lot of other examples if you do a google search like this one.

you also said the claims show that they don't actually happen inside the inner event horizon of the Kerr metric for a rotating black hole,do they appear in some other region of a black hole or not at all?

According to the author of that paper, not at all.

 

[twoface42]

i was also told that kerr's metric doesn't take into consideration quantum mechanics,is that why most people think quantum gravity will eliminate ctc's?

 

[JesseM]

i was also told that kerr's metric doesn't take into consideration quantum mechanics,is that why most people think quantum gravity will eliminate ctc's?

It's why it's seen as a possibility that quantum gravity might give different predictions about CTCs, but there are more specific hints that CTCs will be ruled out by quantum gravity too--did you read the links in my first post, or in the post by George Jones? I would also be curious about the answer to George Jones' question about what level you are in school.

 

[twoface42]

i am in my 2nd year of college.is there anything else used against ctc's?

 

[JesseM]

i am in my 2nd year of college.

And what is the specific class that this is for? What's your exact assignment? What types of sources are you expected to use to research it?

 

[twoface42]

you said quantum mechanics might give different predictions on ctc's,what kind?

 

[JesseM]

you said quantum mechanics might give different predictions on ctc's,what kind?

Just that they won't occur at all, usually because when QM or perturbations are added to GR solutions containing them, quantities like energy go to infinity on the boundary of the region where the GR solution predicts CTCs can occur, which means GR's predictions about anything beyond that boundary are likely to be badly off. See the page I linked to earlier on the infinite blueshift of incoming waves (electromagnetic or gravitational) on the inner horizon of the Kerr black hole, for instance. And if you're indeed researching this for a school paper you could check out Stephen Hawking's chapter of the book https://www.amazon.com/dp/0393020223/?tag=pfamazon01-20 which talks about how quantum theory also may a prediction of infinite energy densities on Cauchy horizons which contain CTCs. When is your project due, anyway? And before addressing any further questions about CTCs, I would ask that you first answer the questions I asked you earlier:

And what is the specific class that this is for? What's your exact assignment? What types of sources are you expected to use to research it?

 

[twoface42]

it's special and general relativity class,and I am supposed to get all the info on the solution's of GR

 

[JesseM]

it's special and general relativity class,and I am supposed to get all the info on the solution's of GR

But you're not required to understand any of the math of these solutions? And where are you supposed to get the information? Presumably they don't expect you to do all the research on online forums.

 

[twoface42]

i was given this,what does this mean? The Kerr vacuum is unobjectionable and realistic (for black hole models) in the exterior regions, and unobjectionable but perhaps unrealistic (for black hole models) in the "shallow interior" regions, but as several commentators have mentioned, it is objectionable in the "deep interior" regions, since it there admits closed timelike curves (CTCs), as does the Goedel lambdadust. These CTCs are problematical.

 

[JesseM]

Could you answer my questions about the nature of the assignment? And how soon is it due? If not too soon they probably want you to look at some actual books...

 

[twoface42]

thursday and present on friday.

 

[George Jones]

i was also told that kerr's metric doesn't take into consideration quantum mechanics,is that why most people think quantum gravity will eliminate ctc's?

Take a look at this paper and the works that it references:

http://arxiv.org/abs/gr-qc/0204022.

Also, according to the work of Poisson and Israel, classical physics might block the formation of closed timelike curves in Kerr spacetime. They show that a test fluid that has fallen into the black hole has an energy density that diverges at the inner (Cauchy) horizon according to some local observers. Problem 3 on pages 217-18 of Poisson's book A Relativist's Toolkit: The Mathematics of Black-Hole Mechanics demonstrates this for a Reissner-Nordstrom black hole, which has a Cauchy horizon, but which doesn't have closed timelike curves. Poisson hints that the situation is similar for Kerr, but a little more complicated mathematically.

When looking for information on Kerr black holes and CTCs, I came across this paper which suggests that the apparent CTCs are just an artifact of a bad choice of coordinates, and with a different choice they disappear (and so are not really physical):

http://arxiv.org/abs/gr-qc/0207014

If you feel like giving it a once-over, I'd be interested to know if you think the argument can be dismissed out of hand, or if there could possibly be something to it.

This looks interesting, but I'm not sure when/if I'll be able to have a close look at it. As you (Jesse) said, caution is needed. Since this is an extraordinary result for which a journal reference can't be found, I suspect this paper has been rejected by several journals. The abstract statement

In addition, it is demonstrated that the possible causality violation thus far regarded to occur near the ring singularity via the development of closed timelike curves there is not really an unavoidable pathology which has plagued the Kerr-Newman solution but simply a gauge (coordinate) artifact as it disappears upon transforming from Boyer-Lindquist to the new time coordinate.

to me seems impossible. Kerr-Newman is a maximally extended spacetime and changing coordinates does not change the causal character of a curve.

Wormholes can also be used to generate closed timelike curves, but wormholes require exotic material. I wrote about Morris-Thorne wormholes and closed timelike curves here:

http://groups.google.ca/group/sci.physics.research/msg/ca7fd4ed9d282afb?dmode=source;

http://groups.google.ca/group/sci.physics.research/msg/37fc731263f506eb?dmode=source.

 

[twoface42]

would ctc's split other universes?

 

[twoface42]

george jones,so those two authors you told say classical physics will prevent ctc's from forming?

 

[JesseM]

thursday and present on friday.

And how long ago were you first given this assignment? Unless it's very short-term I'd think your professor would expect you to have read some books for it rather than just asking questions online.

 

[twoface42]

i was given 2 months but GR was the last part of my project becuase it was the hardest.the last post george jones gave me,it does say that classical physics prevents ctc's? JesseM could you answer post 19 for me please?

 

[JesseM]

i was given this,what does this mean? The Kerr vacuum is unobjectionable and realistic (for black hole models) in the exterior regions, and unobjectionable but perhaps unrealistic (for black hole models) in the "shallow interior" regions, but as several commentators have mentioned, it is objectionable in the "deep interior" regions, since it there admits closed timelike curves (CTCs), as does the Goedel lambdadust. These CTCs are problematical.

"Shallow interior" here just means the region between the outer horizon and the inner horizon, and "deep interior" just means inside the inner horizon. So whoever wrote this is just saying that the region inside the inner horizon is objectionable because it contains CTCs, and a lot of physicists think that CTCs are a sign that something is going wrong with the theory (though this is just speculation, there is no proof that CTCs cannot exist in the real world).

 

[JesseM]

i was given 2 months but GR was the last part of my project becuase it was the hardest.

What was the earlier part of the project, then? And is the GR part specifically on CTCs in Kerr black holes, or is it about broader issues?

the last post george jones gave me,it does say that classical physics prevents ctc's?

His post is just talking about the same issue I discussed in post #16, that even in classical physics, if you model electromagnetic or gravitational waves falling into the hole you get the prediction that their wavelength becomes infinitely short (infinitely blueshifted) on the inner horizon, a type of singularity (quantity going to infinity) which suggests we may not be able to trust GR's predictions beyond that distance even in classical physics. Then there are additional quantum issues with Cauchy horizons that I mentioned in post #16 (the inner horizon is a type of Cauchy horizon), I definitely recommend reading Hawking's chapter in "The Future of Spacetime" which discusses this (if your professor actually wants you to go into quantum gravity issues--he/she may not even want that level of sophistication, have you asked your professor about this?)

 

[twoface42]

i got down most of the info i needed for SR i just need some info on kerr's metric that's what i was given.

 

[George Jones]

i got down most of the info i needed for SR i just need some info on kerr's metric that's what i was given.

It seems that classical general relativity breaks down at the Cauchy horizon. This has suspected/known for almost 40 years. It also seems that semi-classical relativity breaks down at the Cauchy Horizon. It looks like this means that a fully quantum mechanical theory of gravity is necessary to predict what happens at and inside the Cauchy horizon. Closed timelike curves in the spacetime of a rotating black hole necessarily involve events inside the Cauchy horizon. Without a quantum theory of gravity, it seems that it is impossible to ascertain the status of closed timelike curves in the spacetime of a rotating black hole. Quantum gravity could allow them, or quantum gravity could prohibit them. We just don't know.

Again, I encourage you to read (at least the words of)

http://arxiv.org/abs/gr-qc/0204022

by Matt Visser.

 

[twoface42]

But most think quantum gravity will prevent closed timelike loops?

 

[twoface42]

"Shallow interior" here just means the region between the outer horizon and the inner horizon, and "deep interior" just means inside the inner horizon. So whoever wrote this is just saying that the region inside the inner horizon is objectionable because it contains CTCs, and a lot of physicists think that CTCs are a sign that something is going wrong with the theory (though this is just speculation, there is no proof that CTCs cannot exist in the real world).

what is wrong general relativity or the metric it self?